Is it permissible to give a gift to a friend who was instrumental in bringing work to an institution, and is it permissible to take a commission for finalizing business deals for the same institution?

If your friend receives a salary for his work, it is not permissible for him to accept a gift from your company unless he obtains permission from the employers. As for you, if you do not receive a salary for your work, it is permissible for you to receive a commission from the company owners for finalizing deals for them, and this is considered a legitimate brokerage. If you have contracted with them for the commission, then you are entitled to it; otherwise, it is a gift from them and not obligatory.